CN103163542B - Observation constant based method for detecting gross error in global navigation satellite system (GNSS) baseline solution - Google Patents

Abstract

The invention discloses an observation constant based method for detecting a gross error in global navigation system (GNSS) baseline solution. The method includes firstly calculating a difference value between a double-differenced carrier ionosphere-free combination value and an observation equation calculation value, then performing estimation by using difference values between double-differenced carrier ionosphere-free combination values and observation equation calculation values of prior two epochs to obtain a threshold value of a corresponding difference value of a current epoch, and finally judging whether a carrier observation value of the current epoch contains the gross error by comparing the threshold value with the observation value. According to the observation constant based method, problems that single gross error is difficult to position and continuous gross errors are difficult to detect in GNSS baseline solution are effectively solved.

Description

A kind of Detection of Gross Errors method based on observation constant in GNSS Baselines

Technical field

The present invention relates to Detection of Gross Errors method in Baselines, particularly the Detection of Gross Errors method based on carrier wave observation constant.

Background technology

Baselines is the important content of reference station integrity monitoring.By Baselines and carry out net adjustment, obtain the displacement reduction of each base station, by the coordinate to base station, regularly revise, to guarantee the accuracy of base station coordinate, for user quick and precisely locates and provides safeguard.Detection of Gross Errors is the study hotspot of Baselines quality control, yet, because least square does not have robust, once there is rough error in observed reading, even if number is few, also can net result be produced and be had a strong impact on.Can directly have influence on the precision of blur level floating-point solution and can fix correctly by accurate detection rough error, and then affect the resolving mass of baseline.

Traditional Detection of Gross Errors method is first by least square, asked for blur level floating-point solution and carried out blur level and fix mostly, the residual values generating after fixing based on blur level, uses hypothesis test structure statistical test amount and carries out Detection of Gross Errors or survey rough error by robust estimation model.Yet, due to least-square residuals statistical dependence, covered the inner link between rough error and residual values, rough error cannot be correctly reflected in corresponding residual values to be gone, this just makes the statistical test amount based on residual values cannot correct detection rough error, due to number of satellite restriction, cause in two poor carrier wave observation equations redundant observation less, robust estimation model is reduced greatly to the susceptibility of rough error.Therefore, the location of the Detection of Gross Errors based on residual values becomes quite difficult.

Summary of the invention

Research Thinking different from the past, herein for survey at present the deficiency of rough error based on residual values, has proposed a kind of Detection of Gross Errors method based on carrier wave observation constant, has effectively solved single rough error location difficulty, continuously the problem of Detection of Gross Errors difficulty.

The rough error determination methods that the present invention proposes, it is characterized in that building two poor carrier waves without the difference of ionosphere combined value and observation equation calculated value, by using the first two two poor carrier waves epoch to estimate the threshold value of current epoch of corresponding difference without the difference of ionosphere combined value and observation equation calculated value, thereby judge current epoch, whether carrier observations contained rough error.By following step, realize:

(1) build two poor carrier waves without ionosphere combined value equation:

（1.1）

Wherein, for two poor operators; f ₁and f ₂be respectively L ₁, L ₂(satellite carrier signals of two kinds of different frequencies) carrier frequency; with be respectively L ₁, L ₂carrier phase observation data; λ _wfor wide lane ambiguity; ρ is for defending distance, and in pseudorange single-point location, precision is meter level; O, M are respectively orbit error and multipath effect, in two eikonal equations, can ignore; T is tropospheric delay, with the correction of the UNB3m of University of New Brunswick Tropospheric Models; N ₁and N ₂be respectively L ₁, L ₂carrier wave blur level.In formula (1.1), when all parameters are all exact value, equation is set up.Formula (1.1) the equal sign left side be two poor carrier waves without ionosphere combined value, calculated value is combined without ionosphere for two poor carrier waves in equal sign the right.Due to L ₁, L ₂the precision of carrier observations is 0.01 week, so the equal sign left side can be considered as exact value, and equal sign the right is owing to being subject to two poor distances of defending two poor tropospheres the impact of parameters precision, has certain deviation with the two poor carrier waves of levoform without ionosphere combined value.

(2) by using the first two two poor carrier waves epoch to do to estimate without the difference of ionosphere combined value and observation equation calculated value, obtain the threshold value of current epoch of corresponding difference:

Therefore in Baselines, the coordinate of base station is accurately known, and two poor distance precision of defending depend primarily on rover station and defend distance.Rover station is defended distance and can be tried to achieve by co-ordinates of satellite and the rover station pseudorange single-point elements of a fix:

$\widehat{\mathrm{\ρ}}=\sqrt{{\{X^i-(X_r+\mathrm{\ΔX})\}}^2+{\{Y^i-(Y_r+\mathrm{\ΔY})\}}^2+{\{Z^i-(Z_r+\mathrm{\ΔZ})\}}^2}---\left(1.2\right)$

Wherein, for the rover station of gained is as calculated defended distance; X ⁱ, Y ⁱ, Z ⁱbe respectively the coordinate of i satellite; X _r, Y _r, Z _rbe respectively rover station r coordinate (whether rover station yes represents with r) true value; △ X, △ Y, △ Z are respectively pseudorange single-point and locate the coordinate (rover station whether identical with above rover station of the rover station here yes) of the rover station r obtaining compared to the deviator of rover station coordinate true value.

From formula (2.2), temporal evolution size is affected by co-ordinates of satellite variable quantity only.At adjacent moment t _k, t _{k+ △ k}, rover station is defended distance variable quantity and is:

$\mathrm{\Δ}\widehat{\mathrm{\ρ}}\left(\begin{array}{cc}{t}_k& t_{k+\mathrm{\Δk}}\end{array}\right)=\sqrt{\widehat{\mathrm{\ρ}}{\left(t_k\right)}^2+2\mathrm{\Δt}(V_X\·X+V_Y\·Y+V_Z\·Z)+{\mathrm{\Δ}}^2}-\widehat{\mathrm{\ρ}}\left(t_k\right)---\left(1.3\right)$

Wherein, $\mathrm{\Δ}\widehat{\mathrm{\ρ}}\left(\begin{array}{cc}{t}_k& t_{k+\mathrm{\Δk}}\end{array}\right)$ For (t _k, t _{k+ △ k}) rover station is defended the variation of distance in the time period; for t _kconstantly defend distance; △ t=t _{k+ △ k}-t _k; V _x, V _y, V _zbe respectively satellite at (t _k, t _{k+ △ k}) the interior average velocity along X, Y, Z axis of time period; X=X ⁱ-(X _r+ △ X), Y=Y ⁱ-(Y _r+ △ Y), Z=Z ⁱ-(Z _r+ △ Z), △ ²=△ X ²+ △ Y ²+ △ Z ².

From analyzing, it is relevant with rover station coordinate deviator size along change in coordinate axis direction speed with satellite that rover station is defended distance variable quantity.Due at short notice, satellite is almost constant and rover station coordinate deviator is constant along the speed of change in coordinate axis direction, therefore can think in the short time that rover station is defended distance variable quantity approximately equal, $\mathrm{\Δ}\widehat{\mathrm{\ρ}}\left(\begin{array}{cc}{t}_{k-\mathrm{\Δk}}& t_k\end{array}\right)\≈\mathrm{\Δ}\widehat{\mathrm{\ρ}}\left(\begin{array}{cc}{t}_k& t_{k+\mathrm{\Δk}}\end{array}\right).$ The impact that rover station coordinate deviator combines calculated value on two poor carrier waves without ionosphere is cumulative property in time.Therefore in the situation that L1, L2 carrier wave do not have rough error, differ from carrier waves without the difference approximately equal of ionosphere combined value and observation equation calculated value adjacent epoch pair, and be obvious linear feature, that is: $\mathrm{\Δ}\▿P(j+1)-\mathrm{\Δ}\▿P\left(j\right)\≈\mathrm{\Δ}\▿P\left(j\right)-\mathrm{\Δ}\▿P(j-1)$ （1.4）

Wherein, be to differ from carrier waves without the difference of ionosphere combined value and observation equation calculated value j+1 epoch pair.

Utilize the first two known epoch be worth into interpolation, obtain the valuation of current epoch:

$\mathrm{\Δ}\▿\tilde{P}(j+1)\≈2\·\mathrm{\Δ}\▿P\left(j\right)-\mathrm{\Δ}\▿P(j-1)---\left(1.5\right)$

Wherein, it is j+1 epoch valuation; with be respectively j and j-1 epoch true value.If there is rough error j+1 epoch, utilize with interpolation goes out the valuation of j+2 epoch the like.

(3) judge current epoch, whether carrier observations contained rough error:

Due to from formula (1.1), work as L ₁, L ₂while there is rough error in (satellite carrier signals of two kinds of different frequencies) carrier wave, rough error by respectively reduced 0.562 times be reflected to 0.438 times in.In order to detect 0.1 week above rough error, now threshold value is made as when time, think in observed reading and do not contain rough error, otherwise think and contain rough error.

Detection of Gross Errors method based on observation constant in the GNSS Baselines proposing by the present invention, effectively having solved single rough error in GNSS Baselines cannot locate, continuously the problem of Detection of Gross Errors difficulty.

Accompanying drawing explanation

Fig. 1 is the Detection of Gross Errors process flow diagram based on observation constant in Baselines.

Fig. 2 is that P346 station adds after single rough error true value and its threshold value.

Fig. 3 is that P346 station adds after single rough error true value exceeds upper threshold situation, by the difference of upper threshold and true value, represents.

Fig. 4 is that P346 station adds after continuous rough error true value and its threshold value.

Fig. 5 is that P346 station adds after continuous rough error true value exceeds threshold value lower limit situation, for the difference of threshold value lower limit and true value represents.

Embodiment

The Detection of Gross Errors method based on observation constant that the present invention proposes is implemented as follows:

(1) pseudorange single-point location obtains the rough coordinates of rover station;

(2) with UNB3m model, troposphere is revised;

(3) rover station rough coordinates and tropospheric delay are brought into formula (1.1) equal sign right side, ignore orbit error and multipath effect, obtain two poor carrier waves without the calculated value of ionosphere combination;

(4) L1, L2 carrier observations are brought into formula (1.1) left side, try to achieve two poor carrier waves without ionosphere combined value;

(5) ask for described two poor carrier wave without the difference of ionosphere combined value and observation equation calculated value with the first two epoch value is carried out linear interpolation and is asked for current epoch threshold value

(6) calculate current epoch value and threshold value compare, judge whether to contain rough error.

Embodiment mono-

Validity for the Detection of Gross Errors method of proof based on observation constant, choose (Columbia Univ USA station, U.S. CORS net CMBB station below, be positioned at California, COLUMBIACOLLEGE, CA, USA) with (U.S. La Bote station, P346 station, be positioned at the state of Indiana, LaPorte, CA, USA) baseline of 15 minutes " totally " of on April 23rd, 2011 data composition is tested, base length 200km, wherein CMBB(Columbia Univ USA stands, be positioned at California, COLUMBIACOLLEGE, CA, USA) be base station, P346 is rover station.Take G08 satellite as reference star, and choosing G03 satellite is research object.

Build two poor carrier waves without ionosphere combined value equation:

（1.1）

Wherein, for two poor operators; f ₁and f ₂be respectively L ₁, L ₂(satellite carrier signals of two kinds of different frequencies) carrier frequency; with be respectively L ₁, L ₂carrier phase observation data; λ _wfor wide lane ambiguity; ρ is for defending distance, and in pseudorange single-point location, precision is meter level; O, M are respectively orbit error and multipath effect, in two eikonal equations, can ignore; T is tropospheric delay, with the correction of the UNB3m of University of New Brunswick Tropospheric Models; N ₁and N ₂be respectively L ₁, L ₂carrier wave blur level.In formula (1.1), when all parameters are all exact value, equation is set up.Formula (1.1) the equal sign left side be two poor carrier waves without ionosphere combined value, calculated value is combined without ionosphere for two poor carrier waves in equal sign the right.Due to L ₁, L ₂the precision of carrier observations is 0.01 week, so the equal sign left side can be considered as exact value, and equal sign the right is owing to being subject to two poor distances of defending two poor tropospheres the impact of parameters precision, has certain deviation with the two poor carrier waves of levoform without ionosphere combined value.

(2) by using the first two two poor carrier waves epoch to do to estimate without the difference of ionosphere combined value and observation equation calculated value, obtain the threshold value of current epoch of corresponding difference:

Therefore in Baselines, the coordinate of base station is accurately known, and two poor distance precision of defending depend primarily on rover station and defend distance.Rover station is defended distance and can be tried to achieve by co-ordinates of satellite and the rover station pseudorange single-point elements of a fix:

$\widehat{\mathrm{\ρ}}=\sqrt{{\{X^i-(X_r+\mathrm{\ΔX})\}}^2+{\{Y^i-(Y_r+\mathrm{\ΔY})\}}^2+{\{Z^i-(Z_r+\mathrm{\ΔZ})\}}^2}---\left(1.2\right)$

Wherein, for the rover station of gained is as calculated defended distance; X ⁱ, Y ⁱ, Z ⁱbe respectively the coordinate of i satellite; X _r, Y _r, Z _rbe respectively rover station r coordinate (whether rover station yes represents with r) true value; △ X, △ Y, △ Z are respectively pseudorange single-point and locate the coordinate (rover station whether identical with above rover station of the rover station here yes) of the rover station r obtaining compared to the deviator of rover station coordinate true value.

From formula (2.2), temporal evolution size is affected by co-ordinates of satellite variable quantity only.At adjacent moment t _k, t _{k+ △ k}, rover station is defended distance variable quantity and is:

$\mathrm{\Δ}\widehat{\mathrm{\ρ}}\left(\begin{array}{cc}{t}_k& t_{k+\mathrm{\Δk}}\end{array}\right)=\sqrt{\widehat{\mathrm{\ρ}}{\left(t_k\right)}^2+2\mathrm{\Δt}(V_X\·X+V_Y\·Y+V_Z\·Z)+{\mathrm{\Δ}}^2}-\widehat{\mathrm{\ρ}}\left(t_k\right)---\left(1.3\right)$

Wherein, $\mathrm{\Δ}\widehat{\mathrm{\ρ}}\left(\begin{array}{cc}{t}_k& t_{k+\mathrm{\Δk}}\end{array}\right)$ For (t _k, t _{k+ △ k}) rover station is defended the variation of distance in the time period; for t _kconstantly defend distance; △ t=t _{k+ △ k}-t _k; V _x, V _y, V _zbe respectively satellite at (t _k, t _{k+ △ k}) the interior average velocity along X, Y, Z axis of time period; X=X ⁱ-(X _r+ △ X), Y=Y ⁱ-(Y _r+ △ Y), Z=Z ⁱ-(Z _r+ △ Z), △ ²=△ X ²+ △ Y ²+ △ Z ².

From analyzing, it is relevant with rover station coordinate deviator size along change in coordinate axis direction speed with satellite that rover station is defended distance variable quantity.Due at short notice, satellite is almost constant and rover station coordinate deviator is constant along the speed of change in coordinate axis direction, therefore can think in the short time that rover station is defended distance variable quantity approximately equal, $\mathrm{\Δ}\widehat{\mathrm{\ρ}}\left(\begin{array}{cc}{t}_{k-\mathrm{\Δk}}& t_k\end{array}\right)\≈\mathrm{\Δ}\widehat{\mathrm{\ρ}}\left(\begin{array}{cc}{t}_k& t_{k+\mathrm{\Δk}}\end{array}\right).$ The impact that rover station coordinate deviator combines calculated value on two poor carrier waves without ionosphere is cumulative property in time.Therefore in the situation that L1, L2 carrier wave do not have rough error, differ from carrier waves without the difference approximately equal of ionosphere combined value and observation equation calculated value adjacent epoch pair, and be obvious linear feature, that is: $\mathrm{\Δ}\▿P(j+1)-\mathrm{\Δ}\▿P\left(j\right)\≈\mathrm{\Δ}\▿P\left(j\right)-\mathrm{\Δ}\▿P(j-1)$ （14）

Wherein, be to differ from carrier waves without the difference of ionosphere combined value and observation equation calculated value j+1 epoch pair.

Utilize the first two known epoch be worth into interpolation, obtain the valuation of current epoch:

$\mathrm{\Δ}\▿\tilde{P}(j+1)\≈2\·\mathrm{\Δ}\▿P\left(j\right)-\mathrm{\Δ}\▿P(j-1)---\left(1.5\right)$

Wherein, it is j+1 epoch valuation; with be respectively j and j-1 epoch true value.If there is rough error j+1 epoch, utilize with interpolation goes out the valuation of j+2 epoch the like.

(3) judge current epoch, whether carrier observations contained rough error:

Due to from formula (1.1), work as L ₁, L ₂while there is rough error in carrier wave, rough error by respectively reduced 0.562 times be reflected to 0.438 times in.In order to detect 0.1 week above rough error, now threshold value is made as when $|\mathrm{\&Delta;}\&dtri;\tilde{P}(j+1)-\mathrm{\&Delta;}\&dtri;P(j+1)|<0.04$ Time, think in observed reading and do not contain rough error, otherwise think and contain rough error.

More than build pseudorange single-point positioning equation, ask for P346 station rough coordinates, with UNB3m model, ask for CMBB station and P346 station tropospheric delay value.It is two poor without ionosphere carrier combination value (formula 1.1) to build, and calculates two poor carrier waves without the difference of ionosphere combined value and observation equation calculated value with the first two epoch with carry out interpolation, obtain differing from carrier waves without the valuation of ionosphere combined value and observation equation calculated value difference current epoch pair (formula 1.5), setting threshold judge and in carrier observations, whether contain rough error current epoch.

For the Detection of Gross Errors method of proof based on observation constant has good effect to surveying single rough error with continuous rough error, now experiment is divided into two parts:

Experiment one: in the 11st epoch of P346 station, add respectively the rough error of 0.1,0.2,0.3 week the 21st epoch, the 31st epoch, calculate corresponding epoch two poor carrier waves without the threshold value of ionosphere combined value and observation equation calculated value difference and true value as shown in Figure 1, Fig. 2 exceeds the situation of upper threshold (lower limit) for pair difference carrier waves without the true value of the difference of ionosphere combined value and observation equation calculated value.

Experiment two: stand and add respectively-0.1 ,-0.2 ,-0.3 week rough error 10th～12,20～22,30～32 epoch at P346, calculate corresponding epoch two poor carrier waves without the threshold value of ionosphere combined value and observation equation calculated value difference and true value as shown in Figure 3, Fig. 4 exceeds the situation of upper threshold (lower limit) for pair difference carrier waves without the true value of ionosphere combined value and observation equation calculated value difference.

By experiment one, experiment two can find, the Detection of Gross Errors method based on observation constant to survey single rough error and continuously rough error have good effect.

The above is only the preferred embodiment of the present invention; be noted that for those skilled in the art; under the premise without departing from the principles of the invention, can also make the some improvements and modifications that can expect, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (2)

1. In GPS (Global Position System) GNSS Baselines based on observation constant a Detection of Gross Errors method, it is characterized in that:

   (1) pseudorange single-point location obtains the rough coordinates of rover station;

   (2) with UNB3m model, troposphere is revised;

   (3) according to rover station rough coordinates and tropospheric delay, and ignore orbit error and multipath effect, obtain two poor carrier waves without the calculated value of ionosphere combination;

   (4) according to L1, L2 carrier observations, try to achieve two poor carrier waves without ionosphere combined value, wherein L1, L2 are the satellite carrier signal of two kinds of different frequencies;

   (5) difference without ionosphere combined value and observation equation calculated value by described two poor carrier waves with the first two epoch value is carried out linear interpolation and is asked for current epoch threshold value

   Wherein two poor carrier waves without ionosphere combined value equation are:

   Wherein, for two poor operators; f ₁and f ₂be respectively L ₁, L ₂carrier frequency, wherein L1, L2 are the satellite carrier signal of two kinds of different frequencies; with be respectively L ₁, L ₂carrier phase observation data; λ _wfor wide lane ambiguity; ρ is for defending distance, and in pseudorange single-point location, precision is meter level; O, M are respectively orbit error and multipath effect, in two eikonal equations, can ignore; T is tropospheric delay, with the correction of the UNB3m of University of New Brunswick Tropospheric Models; N ₁and N ₂be respectively L ₁, L ₂carrier wave blur level, in formula (1.1), when all parameters are all exact value, equation is set up;

   Formula (1.1) the equal sign left side be two poor carrier waves without ionosphere combined value, calculated value is combined without ionosphere for two poor carrier waves in equal sign the right, due to L ₁, L ₂the precision of carrier observations is 0.01 week, so the equal sign left side can be considered as exact value, and owing to being subject to two poor distances of defending two poor tropospheres the impact of parameters precision, equal sign the right has certain deviation with the two poor carrier waves in levoform limit without ionosphere combined value;

   (6) by current epoch value and threshold value compare, from judging whether to contain rough error.
2. 2. the Detection of Gross Errors method based on observation constant in GPS (Global Position System) GNSS Baselines as claimed in claim 1, wherein by described two carrier waves that differ from without the difference of ionosphere combined value and observation equation calculated value with the first two epoch value is carried out linear interpolation and is asked for current epoch threshold value for:

   Therefore in Baselines, the coordinate of base station is accurately known, and two poor distance precision of defending depend primarily on rover station and defend distance, and rover station is defended distance and can be tried to achieve by co-ordinates of satellite and the rover station pseudorange single-point elements of a fix:

   Wherein, for the rover station of gained is as calculated defended distance; X ⁱ, Y ⁱ, Z ⁱbe respectively the coordinate of i satellite; X _r, Y _r, Z _rbe respectively rover station r coordinate true value; Δ X, Δ Y, Δ Z are respectively pseudorange single-point and locate the coordinate of the rover station r obtaining compared to the deviator of rover station coordinate true value, from formula (1.2), temporal evolution size is affected by co-ordinates of satellite variable quantity only; At adjacent moment t _k, t _{k+ Δ k}, rover station is defended distance variable quantity and is:

   Wherein, for (t _k, t _{k+ Δ k}) rover station is defended the variation of distance in the time period; for t _kconstantly defend distance; Δ t=t _{k+ Δ k}-t _k; V _x, V _y, V _zbe respectively satellite at (t _k, t _{k+ Δ k}) the interior average velocity along X, Y, Z axis of time period; X=X ⁱ-(X _r+ Δ X), Y=Y ⁱ-(Y _r+ Δ Y), Z=Z ⁱ-(Z _r+ Δ Z), Δ ²=Δ X ²+ Δ Y ²+ Δ Z ²;

   From analyzing, it is relevant with rover station coordinate deviator size along change in coordinate axis direction speed with satellite that rover station is defended distance variable quantity, due at short notice, satellite is almost constant and rover station coordinate deviator is constant along the speed of change in coordinate axis direction, therefore can think in the short time that rover station is defended distance variable quantity approximately equal, the impact that rover station coordinate deviator combines calculated value on two poor carrier waves without ionosphere is cumulative property in time, therefore in the situation that L1, L2 carrier wave do not have rough error, adjacent epoch, two carrier waves that differ from were without the difference approximately equal of ionosphere combined value and observation equation calculated value, and be obvious linear feature, that is:

   Wherein, be to differ from carrier waves without the difference of ionosphere combined value and observation equation calculated value j+1 epoch pair;

   Utilize the first two known epoch be worth into interpolation, obtain the valuation of current epoch:

   Wherein, it is j+1 epoch valuation; with be respectively j and j-1 epoch true value, if there is rough error j+1 epoch, utilize with interpolation goes out the valuation of j+2 epoch the like.